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Fundam. Prikl. Mat., 2019, Volume 22, Issue 4, Pages 101–114 (Mi fpm1818)  

Tame and wild automorphisms of differential polynomial algebras of rank $2$

B. A. Duisengaliyevaa, A. S. Naurazbekovaa, U. U. Umirbaevb

a L. N. Gumilyov Eurasian National University, Astana
b Wayne State University, Detroit, MI

Abstract: It is proved that the tame automorphism group of a differential polynomial algebra $k\{x,y\}$ over a field $k$ of characteristic $0$ in two variables $x$$y$ with $m$ commuting derivations $\delta_1, \ldots, \delta_m$ is a free product with amalgamation. An example of a wild automorphism of the algebra $k\{x,y\}$ in the case of $m\geq 2$ derivations is constructed.

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UDC: 512.5

Citation: B. A. Duisengaliyeva, A. S. Naurazbekova, U. U. Umirbaev, “Tame and wild automorphisms of differential polynomial algebras of rank $2$”, Fundam. Prikl. Mat., 22:4 (2019), 101–114

Citation in format AMSBIB
\Bibitem{DuiNauUmi19}
\by B.~A.~Duisengaliyeva, A.~S.~Naurazbekova, U.~U.~Umirbaev
\paper Tame and wild automorphisms of differential polynomial algebras of rank~$2$
\jour Fundam. Prikl. Mat.
\yr 2019
\vol 22
\issue 4
\pages 101--114
\mathnet{http://mi.mathnet.ru/fpm1818}


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  • Фундаментальная и прикладная математика
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